Various types of distortion and noise are introduced into data signals that are transmitted over a communication path. The distortion and noise is due to interference with other signals within the same frequency range and path and also due to multipath dispersions. Multipath dispersions occur when signals propagate along different or reflected paths through a transmission medium to a receiving destination. Therefore, the signal received is not the same as the original signal transmitted, and when the signal is demodulated and decoded, errors in the original transmitted data often result.
The effect of the interference is to alter or distort the signal spectrum when compared to the spectrum as transmitted. The effects are different at different frequencies across the signaling band. At some frequencies, multipath signals add constructively to result in an increased signal amplitude, while at other frequencies the multipath signals add destructively (out of phase) to cancel or partially cancel the signal, resulting in reduced signal amplitude. Collectively, the wireless environment can be thought of as a channel characterized with frequency selective fading and delay distortion. The effects of the wireless channel over which they were sent have perturbed the recovered tones.
Mathematically, the wireless channel has a transfer function with a corresponding frequency response. Tones have been modified in amplitude and phase by the wireless transfer function. The channel distortions introduce errors in data decoding. Therefore, it is necessary to estimate the amplitude and phase of the transmission channel at each frequency of interest and compensate for the channel in the data decoding process. The estimation of the channel transmission amplitude and phase is termed channel estimation. Therefore, a channel estimation procedure is used to estimate the amplitude and phase of the channel at each tone.
The channel estimation procedure computes a complex valued channel response at each tone location. The channel response is adjusted as necessary to account for signal interference. Generally, the channel response can be adjusted for phase offsets or phase shifts and amplitude changes. The channel responses are collectively combined into a channel frequency response, which is often referred to as a channel estimate.
In a noise free, ideal environment, the phase offset will be zero. However, in the real world, there will be some phase shift or phase offset. However, determining a phase offset is, typically, a computationally expensive process. The phase shift computation generally requires computing and evaluating trigonometric functions. Thus, the computation requires a large number of processor cycles. Even with today's DSPs, real time computation of the large number of calculations requires the use of a cost prohibitive processor or DSP.